document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209724>Question 1209724</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let p, q, r, and s be the roots of g(x) = 3x^4 - 8x^3 + 5x^2 + 2x - 17 - 2x^4 + 10x^3 + 11x^2 + 18x - 14.<BR>\n" );
document.write( "Compute p^2 qrs + pq^2 rs + pqr^2 s + pqrs^2.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #850024 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52781)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=850024\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "Let p, q, r, and s be the roots of g(x) = 3x^4 - 8x^3 + 5x^2 + 2x - 17 - 2x^4 + 10x^3 + 11x^2 + 18x - 14.<BR>\n" );
document.write( "Compute p^2*qrs + pq^2*rs + pqr^2*s + pqrs^2. <BR>\n" );
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document.write( "Reduce the polynomial to the standard form, combining like terms\r\n" );
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document.write( "    3x^4 - 8x^3 + 5x^2 + 2x - 17 - 2x^4 + 10x^3 + 11x^2 + 18x - 14 = x^4 + 2x^3 + 16x^2 + 20x - 31.\r\n" );
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document.write( "Notice that \r\n" );
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document.write( "    p^2*qrs + pq^2*rs + pqr^2*s + pqrs^2 = pqrs*(p + q + r + s).\r\n" );
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document.write( "Also notice that the leading coefficient of the polynomial standard form at x^4 is 1.\r\n" );
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document.write( "Due to Vieta's theorem\r\n" );
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document.write( "    pqrs          = -31  (the product of the roots is equal to the constant term)\r\n" );
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document.write( "    p + q + r + s =  -2  (the sum of the roots is the coefficient at x^3 with the opposite sign).\r\n" );
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document.write( "Therefore,\r\n" );
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document.write( "    p^2*qrs + pq^2*rs + pqr^2*s + pqrs^2 = (-31)*(-2) = 62.\r\n" );
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document.write( "<U>ANSWER</U>.  p^2*qrs + pq^2*rs + pqr^2*s + pqrs^2 = 62.\r\n" );
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document.write( "At this point, the problem is solved completely.\r<BR>\n" );
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document.write( "Edwin, I explain it to you, again.\r<BR>\n" );
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document.write( "The original problem was in this reduced polynomial form.\r<BR>\n" );
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document.write( "They composed this their monstrous version in order for to create their OWN NEW problem for their web-site.\r<BR>\n" );
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document.write( "- .-.- .-.- .-.- .-.- .-.- .-.- .-.- .-.- .-.- .-.\r<BR>\n" );
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document.write( "Edwin, you ask me HOW do I know.\r<BR>\n" );
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document.write( "First, it is obvious even for hedgehog or for rabbit.\r<BR>\n" );
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document.write( "Second, I have an ability to see through walls.\r<BR>\n" );
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document.write( "Really, I can see what happens on the other side of a wall.\r<BR>\n" );
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document.write( "I can do it not because the rays of light go through a wall.\r<BR>\n" );
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document.write( "I can see, because I know what happens on the other side of a wall.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(using the method of deduction . . . )\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Knowledge is a power.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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